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In paper, we study the representation theory of super $W(2,2)$ algebra${\mathfrak{L}}$. We prove that ${\mathfrak{L}}$ has no mixed irreduciblemodules and give the classification of irreducible modules of intermediateseries. We determinate the conjugate-linear anti-involution of ${\mathfrak{L}}$and give the unitary modules of intermediate series.

Representations of Super $W(2,2)$ algebra $\mathfrak{L}$